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\begin{abstract}

This project considers visualization of $\beta$-reduction graphs in the lambda
calculus. We develop a software tool that can take any term in pure lambda
calculus, generate its $\beta$-reduction graph and visualize it with one of
six different graph visualization algorithms. The tool handles reduction
graphs with infinitely many nodes and edges by drawing finite approximations
in which not all redexes have been reduced to their contracta. 

Examples of $\beta$-reduction graphs drawn with the implemented software along
with the lambda terms that generate them are provided. Several families of
terms correspond to well-known classes of graphs, including: $K_n$; the
$n$-dimensional hypercube; the regular, convex $n$-sided polygon and $n$-sided
prisms.

We conjecture that the tool will be useful both for researchers investigating
properties of reduction graphs as well as for students learning about the lambda
calculus.

\end{abstract}
